Generating convex polyominoes at random

Random Generation of hv-Convex Polyominoes with Given Horizontal Projection

Asymptotic Analysis and Random Sampling of Digitally Convex Polyominoes

Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally, our sampler shows a limit shape for large digitally convex polyominoes. Introduction In discrete ...

Counting k-Convex Polyominoes

We compute an asymptotic estimate of a lower bound of the number of k-convex polyominoes of semiperimeter p. This approximation can be written as μ(k)p4p where μ(k) is a rational fraction of k which up to μ(k) is the asymptotics of convex polyominoes. A polyomino is a connected set of unit square cells drawn in the plane Z × Z [7]. The size of a polyomino is the number of its cells. A central p...

Reconstruction of 2-convex polyominoes

There are many notions of discrete convexity of polyominoes (namely hvconvex [1], Q-convex [2], L-convex polyominoes [5]) and each one has been deeply studied. One natural notion of convexity on the discrete plane leads to the definition of the class of hv-convex polyominoes, that is polyominoes with consecutive cells in rows and columns. In [1] and [6], it has been shown how to reconstruct in ...

Generating Fullerenes at Random

In the present paper a method for generating fullerenes at random is presented. It is based on the well known Stone-Wales (SW) transformation. The method could be further generalised so that other trivalent polyhedra with prescribed properties are generated.